Direct and Inverse Variation
Direct variation means y = kx (y increases proportionally with x). Inverse variation means y = k/x (y decreases as x increases). k is the constant of variation.
What You Need to Know
Key Concept Diagram
Direct variation: y = kx; doubling x doubles y
Inverse variation: y = k/x; doubling x halves y
To find k: substitute a known pair of values
Graph of direct variation is a straight line through origin; inverse variation is a hyperbola
Key Vocabulary
Constant of variation
The constant k in y = kx or y = k/x
Direct variation
A relationship where y is proportional to x
Inverse variation
A relationship where y is proportional to 1/x
Proportional
Having a constant ratio between two quantities
Knowledge Check
Select the correct answer for each question. Click "Check Answer" to see if you are right.
Question 1
If y varies directly with x and y = 12 when x = 3, find k.
Question 2
If y varies inversely with x and y = 5 when x = 4, find y when x = 10.
Question 3
Which graph represents direct variation?
Key Concepts Summary
- ●Direct variation: y = kx; doubling x doubles y
- ●Inverse variation: y = k/x; doubling x halves y
- ●To find k: substitute a known pair of values
- ●Graph of direct variation is a straight line through origin; inverse variation is a hyperbola